Heat a grill to medium heat (you can hold your hand 1 to 2 inches above grill level only 4 to 5 seconds) or set a broiler to high and position a rack 6 inches below the heating element.
In a 2- to 3-quart pan, bring 2 1/2 cups water to a boil. Add rice and 1/2 teaspoon salt. Cover, adjust heat to low, and cook until most of the water is absorbed, about 15 minutes. Turn off heat and let sit 5 minutes. Stir in pesto and 1 1/2 teaspoons lemon zest.
Meanwhile, in a medium bowl toss shrimp with oil, 1/2 teaspoon salt, 1/2 teaspoon lemon zest, and the pepper.
Grill shrimp, turning once, until cooked through, about 3 minutes per side, or broil on a baking sheet about 4 minutes total (no need to turn).
Serve shrimp over rice and top with tomatoes.
Note: Nutritional analysis is per serving.